The UK will deport EU citizens after Brexit if they do not apply for the right to remain in time, Home Office minister Brandon Lewis says.
He told a German newspaper they would have to leave even if they met all the criteria for a residency permit.
Campaign group the3million, which represents EU citizens in the UK, said this was "no way to treat people".
The Home Office said 1.8 million people had applied to the scheme and others have until "at least" December 2020.
It said those with "reasonable grounds" for missing the date would be granted an extension to apply for the right to live and work in the UK.
Currently, EU nationals - and their families - living in the UK by 31 October have until the end of 2020 to apply to the EU Settlement Scheme in the event of a no-deal Brexit, or the end of June 2021 if there is a deal.
The Home Office says it does not have a figure for the number of EU citizens currently living in the UK, but estimates by the Migration Observatory put it at 3.3 million, excluding Irish citizens who have the right to settled status already.
Mr Lewis told Die Welt (in German): "If EU citizens until this point of time have not registered and have no adequate reason for it, then the valid immigration rules will be applied."
When pressed on whether that would include those who met the legal requirements for residence but did not apply in the next 14 months, he replied: "Theoretically yes. We will apply the rules."
Maike Bohn, spokeswoman for the3million, said the organisation had pressed the government "for years" to acknowledge what would happen to those who have not acquired the status in 2021.
"Today, after much wait, it is confirmed that hundreds and thousands of people will be punished with the threat of removal from their home. This is no way to treat people, let alone what was promised," she said.
"Those people who miss the tight deadline will face the full force of the hostile environment."
She said this was the "grim reality" of the government's position, "no matter how many times they repeat the phrase 'EU citizens and their families are our friends, neighbours and colleagues and we want them to stay'".
Those applying for settled status must prove their identity, show they live in the UK and declare any criminal convictions.
Once granted settled status, they can use the NHS, study and access public funds and benefits, as well as travel in and out of the country.
The total number of settlement applications finalised by the end of September was 1.5 million, according to figures released this week by the Home Office.
Of these, 61% were granted settled status and 38% were given pre-settled status, which can be applied to be updated once someone has lived in the country continuously for five years. The conclusion in 0.5% of cases was classed as having "other outcomes".
Lib Deb home affairs spokeswoman Christine Jardine said she was "absolutely appalled" by Brandon Lewis's deportation threat and she predicted "thousands" of people would be left undocumented by the "arbitrary" deadline.
She warned it could create another Windrush-style scandal - when individuals who arrived from Commonwealth countries between 1948 and 1971 were wrongly told they were in the UK illegally, despite living in the country for decades.
"Brandon Lewis has finally confirmed what we've known all along: Boris Johnson has no intention of keeping his promise to automatically guarantee the rights of EU citizens living in the UK," said Ms Jardine.
"That is totally unacceptable."
Mr Lewis tweeted in response to his critics:
My words are somewhat taken out of context. #EUcitizens have till at least Dec 2020 & there’s plenty of help available to apply. We’ve now had 2 million applications & we’ve always said we’ll allow time for those with reasonable grounds for missing the deadline.— Brandon Lewis (@BrandonLewis) October 10, 2019
A statement from the Home Office said: "We have received two million applications and are looking for reasons to grant status, not refuse, and EU citizens have until at least December 2020 to apply.
"We've always been clear that where they have reasonable grounds for missing the deadline, they'll be given a further opportunity to apply."